They're very similar - they both represent social stratification of society into social ranks of wealth, income, race, education, and power.
The only difference is that a person's 'caste' in India, is dictated by blood and can never be changed. Whereas in the West, a person can theoretically transition from one class to another.
https://news.ycombinator.com/item?id=24556347
https://news.ycombinator.com/item?id=24554209